F(t)=sec pi t/4?

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Answer 1 · 2018-04-10T03:57:13

I'm assuming your asking for the derivative or integral since your question is tagged calculus.

Derivative:
#F(t) = sec((pit)/4)#

#F(t) = (cos((pit)/4))^-1#

#F'(t) = -(cos((pit)/4))^-2 xx -sin((pit)/4) xx pi/4#

#F'(t) = (pisin((pit)/4))/(4cos^2((pit)/4))#

#F'(t) = pi/4tan((pit)/4)sec((pit)/4)#

Integral:

#I =int# # sec((pit)/4)# #dt#

#I = int# #sec((pit)/4) xx(sec((pit)/4) + tan((pit)/4))/(sec((pit)/4)+ tan((pit)/4))# #dt#

#I = 4/(pi)int# #(pi/4sec^2((pit)/4) + pi/4sec((pit)/4)tan((pit)/4))/(sec((pit)/4)+ tan((pit)/4))# # dt#

#I = 4/piln(sec((pit)/4) + tan((pit)/4)) + C#